# Born-Oppenheimer potential for H$ 2$ - Physics > Chemical Physics

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Abstract: The Born-Oppenheimer potential for the $^1\Sigma g^+$ state of H$ 2$ isobtained in the range of 0.1 - 20 au, using analytic formulas and recursionrelations for two-center two-electron integrals with exponential functions. Forsmall distances James-Coolidge basis is used, while for large distances theHeitler-London functions with arbitrary polynomial in electron variables. Inthe whole range of internuclear distance about $10^{-15}$ precision isachieved, as an example at the equilibrium distance $r=1.4011$ au theBorn-Oppenheimer potential amounts to $-1.174\,475\,931\,400\,216\,73$.Results for the exchange energy verify the formula of Herring and FlickerPhys. Rev. {\bf 134}, A362 1964 for the large internuclear distanceasymptotics. The presented analytic approach to Slater integrals opens a windowfor the high precision calculations in an arbitrary diatomic molecule.

Author: ** Krzysztof Pachucki**

Source: https://arxiv.org/